# Weakly Aggregative Modal Logic: Characterization and Interpolation (new version)

## TL;DR

This paper explores the foundational model theory of Weakly Aggregative Modal Logic (WAML), providing a characterization theorem and demonstrating the absence of Craig Interpolation in basic systems, with implications for epistemic logic and game theory.

## Contribution

It offers a van Benthem-Rosen style characterization theorem for WAML and proves that basic WAML systems lack Craig Interpolation, advancing understanding of their logical properties.

## Key findings

- Established a bisimulation-based characterization theorem for WAML.
- Proved that basic WAML systems do not have Craig Interpolation.
- Enhanced understanding of WAML's model-theoretic properties.

## Abstract

Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system K_n lacks Craig Interpolation.